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(a) Is there evidence to support the claim that the high- er baking temperature results in wafers with a lower mean photoresist thickness? Use α-0.05. (b) What is the P-value for the test conducted in part (a)? (c) Find a 95 percent confidence interval on the difference in means. Provide a practical interpretation of this interval (d) Draw dot diagrams to assist in interpreting the results from this experiment. (e) Check the assumption of normality of the photoresist thickness. (f) Find the power of this test for detecting an actual dif- ference in means of 2.5 kA (g) What sample size would be necessary to detect an actual difference in means of 1.5 kA with a power of at least 0.922.29. Photoresist is a light-sensitive material applied to semiconductor wafers so that the circuit pattern can be imaged on to the wafer. After application, the coated wafers are baked to remove the solvent in the photoresist mixture and to harden the resist. Here are measurements of photore- sist thickness (in kA) for eight wafers baked at two differ- ent temperatures. Assume that all of the runs were made in andom order. 100 °C 5.263 6.748 7.461 7.015 8.133 7.418 3.772 8.963 95 °C 11.176 7.089 8.097 11.739 11.291 10.759 6.467 8.315

math   Statistics-And-Probability   
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a) State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis. Null hypothesis: ds 0 Alternative hypothesis: d0 Note that these hypotheses constitute a one-tailed test. Formulate an analysls plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a matched-pairs t-test of the null hypothesis Analyze sample data. Using sample data, we compute the standard deviation of the differences (s), the standard error (SE) of the mean difference, the degrees of freedom (DF), and the t statistic test statistic (t) s=sqrt [(2(di-d)2 / (n-1)] s = 2.187 SE /sqrt(n) S.E 0.7733 DF n 1 8-1tI(x1-x2)- D1/SE t3.20 where di is the observed difference for pair i, d is mean difference between sample pairs, D is the 1 (X1-X2) hypothesized mean difference between population pairs, and n is the number of pairs. b) Thus, the P-value 0.007533 Interpret results. Since the P-value (0.007533) Is less than the signlficance level (0.05), we have to reject the null hypothesis. From this we conclude that we have sufficlent evldence that the higher baking temperature results In wafer with a lower mean photoreslst thlckness.95 degree C(A) 100 degree C(B) d (A-B) (di - dbar) 2 9.474084 0.341 4.553956 3.381921 4.724 5.058001 3.1580.466489 3.341 0.749956 0.0484 0.6489.753129 19.8 33.485936 2.475 4.185742 11.176 7.089 8.097 11.739 11.291 10.759 6.467 8.315 74.933 9.366625 5.623 6.748 7.461 7.015 8.133 7.418 3.772 8.963 55.133 5.553 0.636 2.695 Total 6.8916252 Average c) 95% confidence Interval on the difference in means Is C.1 95% confidence interval is given by:- CI = ( C.に2.475 + 2.365 x 0.7733 (0.646145, 4.30385) = 2.475 + 1.82885 C.I (0.646145, 4.30385) d) Dotplot dlagramDotplot of 95 degree C(A), 100 degree C(B) 95 degree C(A) 100 degree C(B) 7.2 8.4 9.6 10.8 12.0 3.6 4.8 6.0 Data

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  • 9. Photoresist is a light-sensitive material applied to semiconductor wafers so that the circuit pattern can...

    9. Photoresist is a light-sensitive material applied to semiconductor wafers so that the circuit pattern can be imaged on to the wafer. After application, the coated wafers are baked to remove the solvent in the photoresist mixture and to harden the resist. Here are measurements of photoresist thickness (in kÅ) for eight wafers baked at two different temperatures. Assume that all of the runs were made in random order 95°C 11.176 7.089 8.097 11.739 11.291 100 °C 5.623 6.748 7.461...

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